{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.io import loadmat\n",
    "import scipy.optimize as opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = loadmat('./ex5data1.mat')\n",
    "# data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "X,y 为训练集\n",
    "\n",
    "Xval,yval 为交叉训练集\n",
    "\n",
    "Xtest,ytest 为测试集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data['X']\n",
    "y = data['y']\n",
    "\n",
    "X_add_one = np.insert(X,0,1,axis=1)\n",
    "\n",
    "Xval = data['Xval']\n",
    "yval = data['yval']\n",
    "\n",
    "Xtest = data['Xtest']\n",
    "ytest = data['ytest']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "((12, 1), (12, 1), (21, 1), (21, 1), (21, 1), (21, 1))"
     },
     "metadata": {},
     "execution_count": 231
    }
   ],
   "source": [
    "X.shape,y.shape,Xval.shape,yval.shape,Xtest.shape,ytest.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Text(0, 0.5, 'Water flowing out of the dam(y)')"
     },
     "metadata": {},
     "execution_count": 232
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(X,y,'rx')\n",
    "plt.xlabel('Change in water level(X)')\n",
    "plt.ylabel('Water flowing out of the dam(y)')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 损失函数(不带正则参数)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(theta,X,y):\n",
    "    #theta (2,)\n",
    "    #X (12,2)\n",
    "    #y (12,1)\n",
    "    m = X.shape[0]\n",
    "    # X@theta -> (12,) 不一定代表就是列向量，(12,) - (12,1)可能会被广播成 (12，12)\n",
    "    inner = X @ theta - y.flatten()  # R(m,)\n",
    "    #assert inner.shape[1]=='','inner.shape = {}'.format(inner.shape)\n",
    "    square_sum = inner.T @ inner\n",
    "    cost = square_sum / (2 * m)\n",
    "\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 损失函数（带正则参数）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costReg(theta,X,y,l=1):\n",
    "    m = X.shape[0]\n",
    "\n",
    "    regularized_term = (l / (2 * m)) * np.power(theta[1:], 2).sum()\n",
    "\n",
    "    return cost(theta, X, y) + regularized_term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [],
   "source": [
    "# theta1 = np.zeros(2)\n",
    "# costReg(theta1,X_add_one,y,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 梯度函数（不带正则）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(theta, X ,y):\n",
    "    #theta (2,1)\n",
    "    #X (12,2)\n",
    "    #y (12,1)\n",
    "    m=len(X)\n",
    "\n",
    "    h = X @ theta #(12,1)\n",
    "    grad =(h - y).T @ X\n",
    "    return grad/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-15.30301567, 598.16741084]])"
     },
     "metadata": {},
     "execution_count": 237
    }
   ],
   "source": [
    "gradient(np.ones((2,1)),X_add_one,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 梯度函数（带正则）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_reg(theta, X, y, l=1):\n",
    "    m=len(X)\n",
    "    _theta = theta.copy()\n",
    "    _theta[0]=0\n",
    "    reg = (l/m)*_theta\n",
    "    return gradient(theta, X, y)+reg.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(1, 2)"
     },
     "metadata": {},
     "execution_count": 239
    }
   ],
   "source": [
    "gradient_reg(np.ones((2,1)), X_add_one, y).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 高级优化函数进行训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_trains(X,y,l):\n",
    "    init_theta = np.zeros(X.shape[1])\n",
    "    res = opt.minimize(fun=costReg,x0=init_theta,args=(X,y.flatten(),l),method='TNC',jac=gradient_reg)\n",
    "    #y要转成 (m,)传进去才能保证不出错。否则会报 输出无效值错误\n",
    "    return res.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[13.08771416],\n       [ 0.367742  ]])"
     },
     "metadata": {},
     "execution_count": 241
    }
   ],
   "source": [
    "linear_theta = linear_trains(X_add_one,y,1).reshape(2,1)\n",
    "linear_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 7.22709892],\n       [ 2.3669394 ],\n       [26.39613099],\n       [26.87516595],\n       [-4.5855357 ],\n       [ 9.79956457],\n       [18.71703246],\n       [ 0.3247627 ],\n       [13.59856456],\n       [-3.23405827],\n       [15.66687341],\n       [21.45853287]])"
     },
     "metadata": {},
     "execution_count": 242
    }
   ],
   "source": [
    "linear_y = X_add_one @ linear_theta\n",
    "linear_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Text(0, 0.5, 'Water flowing out of the dam(y)')"
     },
     "metadata": {},
     "execution_count": 243
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(X,y,'rx')\n",
    "plt.plot(X,linear_y,'b')\n",
    "plt.xlabel('Change in water level(X)')\n",
    "plt.ylabel('Water flowing out of the dam(y)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从图像直接可观察到，用线性回归拟合的效果很差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_costValue(X, y, Xval, yval, l):\n",
    "    x_i = len(X)\n",
    "    \n",
    "    cost_train = []\n",
    "    cost_cv = []\n",
    "    for i in range(1,x_i+1):\n",
    "        theta = linear_trains(X[:i], y[:i], 0)\n",
    "\n",
    "        cost_train.append(costReg(theta, X[:i], y[:i]))\n",
    "        cost_cv.append(costReg(theta, Xval, yval))\n",
    "\n",
    "    return cost_train,cost_cv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([13.85366299,  0.37780979])"
     },
     "metadata": {},
     "execution_count": 245
    }
   ],
   "source": [
    "linear_trains(X_add_one[:10],y[:10],0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_error_curve(X, y, Xval, yval):\n",
    "    error_trains, error_cv = get_costValue(X, y, Xval, yval, 0)\n",
    "\n",
    "    xx = [i for i in range(1,len(X)+1)]\n",
    "    plt.plot(xx, error_trains,'b', label = 'error_trains')\n",
    "    plt.plot(xx, error_cv,'r',label = 'error_cv')\n",
    "    plt.ylim(0,200)\n",
    "    plt.grid(True)\n",
    "    plt.legend(loc=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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8/z689VbUkYiIpEyzkruZ9Y7bnQTU9KR5GrjIzDqYWX/gaODl5EJMs5p2d3WJFJEskkhXyIeBF4GBZlZqZlOBn5jZ62a2HBgPfBvA3d8AHgFWAn8DrnX3qrRFnwpHHQX9+6tLpIhklUZvqLr7xfUU33uA428jtMNnjokTYc4cqKyEdm1r5kERyU5t9wnVeMXFsG0bvPJK1JGIiKSEkjvA6aeHSTzUNCMiWULJHaBHDxg+XMldRLKGknuN4mJYtAi2b486EhGRpCm51yguDjdUFyyIOhIRkaQpudc45RTo2FFNMyKSFZTca+Tnw5gxSu4ikhWU3OMVF8OqVfDBB1FHIiKSFCX3eBqKQESyhJJ7vOOOg0MOUdOMiGQ8Jfd4OTlhKIJ//hPCkMUiIhlJyb2u4mLYuBFWrGj8WBGRVkrJva6JE8NaTTMiksGU3Ovq2xcGDlRyF5GMpuRen+JieO452L076khERJpFyb0+xcWwcye8+GLUkYiINIuSe31OOw1yc9U0IyIZS8m9Pl27wokn6mEmEclYicyhep+ZbTKzFXFlPzWzN81suZk9YWbdYuX9zOxTM1sWW2akM/i0Ki6GxYvh44+jjkREpMkSuXJ/ADizTtlcoMjdhwBvAd+Le+0ddx8WW76WmjAjUFwM1dXw7LNRRyIi0mSNJnd3fw7YUqfsH+5eGdtdBPRJQ2zRGjUKOndWu7uIZCTzBB6zN7N+wJ/dvaie1/4EzHH338eOe4NwNb8N+KG7P9/AZ04HpgMUFhaOmD17dvNqkEZFP/gBndav56VZs/aWlZeXU1BQEGFU6ZXN9VPdMlc21y+Zuo0fP36Ju4+s90V3b3QB+gEr6in/AfAE+74kOgA9YtsjgPeBLo19/ogRI7xV+u//dgf3tWv3Fs2fPz+6eFpANtdPdctc2Vy/ZOoGLPYG8mqze8uY2eXAOcCXYyfB3Xe7e1lsewnwDnBMc88ROQ1FICIZqlnJ3czOBP4dONfdd8aVH2JmubHtAcDRwNpUBBqJz34WDj9cXSJFJOMk0hXyYeBFYKCZlZrZVOBXQGdgbp0uj2OB5Wb2GvAY8DV331LvB2cCs9BrZt48qKqKOhoRkYS1a+wAd7+4nuJ7Gzj2j8Afkw2qVSkuhgcegKVLYWT99y1ERFobPaHamAkTwlrt7iKSQZTcG1NYCEOGqN1dRDKKknsiioth4cIwUqSISAZQck/ExImwZw88X+/zWCIirY6SeyLGjoX27dU0IyIZQ8k9EQcdBKNH66aqiGQMJfdEFRfDa6+RtyVzu+2LSNuh5J6o2FAE3V99NeJAREQap+SeqOHDoXt3ui9ZEnUkIiKNUnJPVG4uTJjAwYsXh0k8RERaMSX3ppg0iQ6bN0NJSdSRiIgckJJ7U0yeTEXnznDPPVFHIiJyQEruTZGfz8aJE+Hxx0G9ZkSkFVNyb6INn/887N4NcVPviYi0NkruTbTjM58JQ//efTckMP+siEgUlNybY9o0eP11WLw46khEROql5N4cF18chiTQjVURaaWU3JujSxe48EJ4+GHYsSPqaERE9pPIHKr3mdkmM1sRV3awmc01szWxdfe4175nZm+b2Woz+1y6Ao/c1KmwfTs8+mjUkYiI7CeRK/cHgDPrlN0IzHP3o4F5sX3MbBBwETA49p7fmFluyqJtTUaPhoED1TQjIq1So8nd3Z8D6nbqPg94MLb9IHB+XPlsd9/t7uuAt4FRKYq1dTELN1ZfeAFWrYo6GhGRWto1832F7r4BwN03mFmvWPnhwKK440pjZfsxs+nAdIDCwkJKMuSR/vLy8r2x5h11FCfn5vLBzTfzzjXXRBtYisTXL9uobpkrm+uXrro1N7k3xOopq7czuLvPBGYCjBw50seNG5fiUNKjpKSEWrGefz59n32Wvg89FGZrynD71S+LqG6ZK5vrl666Nbe3zEYz6w0QW2+KlZcCfeOO6wN82PzwMsDUqbB5M/zpT1FHIiKyV3OT+9PA5bHty4Gn4sovMrMOZtYfOBp4ObkQW7kzzoA+fXRjVURalUS6Qj4MvAgMNLNSM5sK3AEUm9kaoDi2j7u/ATwCrAT+Blzr7lXpCr5VyM2Fq66Cv/8d3nsv6mhERIDEestc7O693T3P3fu4+73uXubuE9z96Nh6S9zxt7n7Ue4+0N2fSW/4rcSVV4b1/fdHG4eISIyeUE2Ffv3CBNr33QdV2f1DRUQyg5J7qkydGppl5s2LOhIRESX3lDnvPOjRQzdWRaRVUHJPlQ4d4LLL4Mkn4aOPoo5GRNo4JfdUmjoVKirgoYeijkRE2jgl91QaPBhOPjk0zWiWJhGJkJJ7qk2dGgYSW7So8WNFRNJEyT3VpkyBggLdWBWRSCm5p1pBAVx0EcyeDdu2RR2NiLRRSu7pMG0a7NwJc+ZEHYmItFFK7ukwahQUFalpRkQio+SeDmbhxurLL8Prr0cdjYi0QUru6XLppWHyjnvvjToSEWmDlNzTpWdPmDQpPNC0a1fU0YhIG6Pknk7TpsGWLWFIAhGRFqTknk6nnx6GA9aNVRFpYUru6ZSTE2ZpmjcP1q2LOhoRaUOU3NPtiitCkr/vvqgjEZE2pNnJ3cwGmtmyuGWbmV1vZjeb2Qdx5Z9PZcAZp29fOPPMMAVfZWXU0YhIG9Hs5O7uq919mLsPA0YAO4EnYi//rOY1d/9rKgLNaNOmwQcfhEm0RURaQKqaZSYA77j7uyn6vOxyzjnQq5durIpIizFPwbjjZnYf8Kq7/8rMbgauALYBi4HvuPvH9bxnOjAdoLCwcMTs2bOTjqMllJeXU1BQ0OT3DZgxgz6PPcaiRx5hz8EHpyGy1Ghu/TKB6pa5srl+ydRt/PjxS9x9ZL0vuntSC9Ae2AwUxvYLgVzCr4LbgPsa+4wRI0Z4ppg/f37z3vjmm+7g/l//ldJ4Uq3Z9csAqlvmyub6JVM3YLE3kFdT0SxzFuGqfWPsy2Kju1e5ezVwNzAqBefIfAMHwpgxmqVJRFpEKpL7xcDDNTtm1jvutUnAihScIztMmwZr1sDzz0cdiYhkuaSSu5kdBBQDj8cV/8TMXjez5cB44NvJnCOrfPGL0KWLbqyKSNolldzdfae793D3T+LKvuLux7n7EHc/1903JB9mljjoILjkEnjsMdi6NepoRCSL6QnVljZtGnz6KTz8cOPHiog0k5J7Sxs+HIYNU9OMiKSVkntLMwtX76++GhYRkTRQco/CJZdAhw6apUlE0kbJPQrdu4eeM7NmhfZ3EZEUU3KPyrRp8Mkn8Mc/Rh2JiGQhJfeonHYafOYzurEqImmh5B4VM5g6FRYsgLfeijoaEckySu5RuvxyyM3VLE0iknJK7lHq3RvOPhsefBAqKqKORkSyiJJ71KZNg3/9C/6qCatEJHWU3KN21lnhCl43VkUkhZTco9auHVx5Zbhy/+CDqKMRkSyh5N4aXHUVVFfDAw9EHYmIZAkl99bgqKNg/PjQa6a6OupoRCQLKLm3FtOmwdq1UFISdSQikgWU3FuLyZPDmDO6sSoiKaDk3lrk58OXvxzGmikrizoaEclwyc6huj42X+oyM1scKzvYzOaa2ZrYuntqQm0Dpk2DPXvCaJEiIklIxZX7eHcf5u4jY/s3AvPc/WhgXmxfEjF0KIwcGZpm3KOORkQyWDqaZc4DHoxtPwicn4ZzZK9p0+D112Hx4qgjEZEMZp7EFaKZrQM+Bhz4rbvPNLOt7t4t7piP3X2/phkzmw5MBygsLBwxe/bsZsfRksrLyykoKEjb5+fu2MEpX/wiGydO5K3vfCdt52lIuusXJdUtc2Vz/ZKp2/jx45fEtZrUkmxyP8zdPzSzXsBc4JvA04kk93gjR470xRlypVpSUsK4cePSe5Irrgg3VjdsgHT+B717N6xfH7pgrlsHmzbxyhFHcMJVV6XvnBFqkX+7iGRz3SC765dM3cysweTeLpmg3P3D2HqTmT0BjAI2mllvd99gZr2BTcmco02aNi2MFPnoo2FoguZyD4OSrVsXEnj8sm5dGO6gzpf7CQB/+Qv86EcwbFhS1RCR6DQ7uZtZJyDH3bfHts8AbgGeBi4H7oitn0pFoG3K6NEwcGCYQLux5L5jR+3kXXe77hythx8OAwbAhAlhPWAA9O8f1u3bs/6GG+j31FPw+ONw7rkhyY+s98JARFqxZK7cC4EnzKzmc/7g7n8zs1eAR8xsKvAe8KXkw2xjzMLV+3e/C2+8AZ0775+4a5ZNdX4YFRSE4QyOOQbOPHNfAh8wAI48MvSnP4D1V15Jv1/8An75S/jZz+CEE+Dznw9J/qST0lhpEUmlZid3d18LDK2nvAyYkExQAlx2GXzve1BUVLs8JweOOCIk63PPrX3lPWAA9OgRvhyS0a1bSObXXQe/+Q3ceSecfDIUF8NNN8Gppyb3+SKSdkm1uUsa9eoFv/1tmF81/uq7b1/Iy2uZGLp0gRtvhG98A2bMgJ/+FMaMCYOc3XRTmOQ72S8SEUkLJffWrLX0WikogH/7N/j612HmTPjJT0KCP/XUkOQnTlSSF2llNLaMJO6gg+D660Nb/69+FbpRnnEGnHIKPPOMnqoVaUWU3KXp8vPh2mvh7bdDc82HH4abrqNGwdNPK8mLtAJK7tJ8HTrA1VfDmjVhPJwtW+C882D48NCVUhOPiERGyV2S1749TJ0Kq1eHh6927IALLggDoT3yCFRVRR2hSJuj5C6p065d6MK5alUYtriqCqZMgeOOC/uVlVFHKNJmKLlL6uXmwiWXhNEt58wJ+5deCoMGhSt7JXmRtFNyl/TJzYULL4TXXgtt8J06hUHRaoZW2LMn6ghFspb6uUv65eTApElw/vnw5z/DLbeE4RW+/W049FA45BDo2bPhdc12QYH604skSMldWo4ZfOELcM458Le/hdEnN2+Gjz4KfeZfeSXsV1TU//4OHWon+wN9EfTsGYZiaKmneUVaGSV3aXlmcNZZYanLHbZvDwm/JvE3tF6/Pmxv3drwubp125vsiyAMqNajR1gOPnjfdvz+QQelqeIiLUfJXVoXszCmTZcuYXTLRFRUQFlZw18Ese0O774LpaXh2J07G/68/Pz9k39DXwQ1S/fu+pUgrYqSu2S+vLzQdn/ooQc8bEn8jDe7doWHrsrKwtLQdllZ6NpZs32gnj5dutRO/gUF4SZyp061t+suDb3Wvn3q/kbS5ii5S9uUnw+HHRaWRLlDeXntxH+gL4gPPggPdNUsB/q1UJ927RL+Uuj/r3/BP/4Rni2oWaqr07dfUBBGLi0sDOv6lm7ddAM8QkruIokyCxOndO4M/fo1/f3V1SHBxyf8mqW8PPHyjz8OzUtxrx2xe3foepqTE9Y1Syr28/LCl2H869u3w8qVUFISvszqk5fXcOKPXwoLw32RRiaSSRv38Itsz56wVFaGf+u6S05O08sipOQu0lJycsIVbxomPV8Q5QTSlZXhvsamTWHZuHHfdvyyenV4re7UjzW6dKk/+ffsSZ81a+Dll8Ok7jVJuGapr6yh8oaOTedgd418CXx2zBhIw7+dkruIJKddu4TueQAhie7YsX/ir/uF8Pbb8L//G740qqv5TPxnmIVuse3b71vq7tcsXbrsX9bQsTXlubnhPNXVId74JQ1lH3foQAJ/uab/szT3jWbWF/gdcChQDcx091+Y2c3AV4GPYod+393/mmygIpIFzPb9ehkwoPHjq6pg61YWvvgip55+eki+7bLrmnRjSQnHpuFzk/krVQLfcfdXzawzsMTM5sZe+5m735l8eCLSpuXmQo8eVBYU6PmDJkpmguwNwIbY9nYzWwUcnqrARESk+VLy+8bM+gHHAy8Bo4FvmNllwGLC1f3HqTiPiEhzuYfHG+J7psava7arq/c9rlAzikX37uH+ZyYxT/IusZkVAAuA29z9cTMrBDYDDvxfoLe77zfTs5lNB6YDFBYWjpg9e3ZScbSU8vJyCtLQ26G1yOb6qW6tiztUVRkVFUZFRQ6VlTns2WNUVuZQUZGzt7yiIoetW/cAndi1K4ddu3LZvTuXXbty+PTT+rd37cqNLTns3p0bey0H9+Z1T8zJcTp3rqBLl0q6dq2gS5eKetddu+57vXPnir33Zg8kmWtKPiQAAAl3SURBVH+78ePHL3H3kfW9llRyN7M84M/A3939rnpe7wf82d2LDvQ5I0eO9MWLFzc7jpZUEmWXsxaQzfVT3ZqvujrMi75iRVjKymr3LNy9u/Z2Y+ua7WR7IObnh6b4mue66ttu7PW6x5rtex5t8+Z96/jt+LLdu+uPzSw8x1Vz9V8zrl38L4KePeHjj1/hqqtOaFb9zazB5J5MbxkD7gVWxSd2M+sda48HmASsaO45RKRluYdeia+/HpJ4zfqNN2o/YFvTw7Cm92B964KCA79ed32g11atWsKYMSNqJeODDiKhK+PmSKQjT83fa+fOA38B1KxLS8PUBps31+7qP378kVy1X9tG8pJpcx8NfAV43cyWxcq+D1xsZsMIzTLrgauTilBE0mL79toJ/PXXwxL/wGmvXmGWxK9+NayPOy5MqNXSLUBm2znuuJY9ZyLM9l39H3FE4u+r+UIoK4Ply9cBvVIeWzK9ZRYC9TVgqU+7tDrl5bBhQz6rVze9CaE5zQ6VldC1676f33V/iseXde2a3pt1e/aEh0NrkndNIn/33X3HdOoERUVhTpWiopDEi4pCcpfUq/nl0bcvbN3awBO7ScqupwFEYrZuhYULYcGCMPzJq69CdfVJzf68+IciD9SUkJ8fmizatYNPPklsQMmcnDCIZCJfBPGDTtZ9lqe6OgxxH38VvmJFSOw1527XLsxyePLJMH36vkR+5JGZ1xtEDkzJXbLCli3w/PMhmS9YAEuXhvbQ9u3hxBPh+9+Hioo3GTLks01u7+3QIbTtJjMOlDts21Z/e2zdsvXrYcmSA9+sg3Czribpf/LJcN5/P3Tnq9GvX0je5567L4kPHKiRhNsKJXfJSJs3w3PP7Uvmy5eHBNqhQ7gqvekmOO00OOkk6NgxvKek5F+MG/fZSOI1C80vXbs2/WZdQ18C8WUVFVVcddW+5pTBg8MvCGm7lNwlI2zcWDuZr4j1werYEU45Bf7jP8LAeqNGhQSfDeJv1h155IGPLSl5LWu7eUrzKLlLq7Rhw75EXlICb74Zyjt1gtGj4eKLQzIfOVLNDCL1UXKXVqG0tHYyX7MmlHfuDKeeCldeGZpZhg/XVKUiiVByl0iUlcFf/rIvma9dG8q7doUxY+Dqq0MyHzYs60Z4FWkR+t9GWow7vPACzJgBjz0WeoJ07x6S+De/GdZDhqTvqUORtkTJXdJu61Z46KGQ1FeuDL04vvrV0NQybJj6V4ukg5K7pIV7mPLyt7+F2bPDWBonnAD33gtTpoQboyKSPkruklLbt8Mf/hCu0pctC0n8K18JbejDh0cdnUjboeQuKbF0abhKnzUrjOMydCj8z//AJZfoYRqRKCi5S7Pt2AFz5oSk/vLL4YGiKVPga18LDxMl87i+iCRHyV2abMWKkNAfeigMjjVoEPziF6H5pXv3qKMTEVBylwTt2gWPPhqS+gsvhKdCv/Sl0JZ+6qm6ShdpbZTc5YBWr4aZM+GBB8LIi0cfDXfeCZdfHkYjFJHWScld9rNnDzzxRLhKnz8/PCE6aVJoSx83Tv3SRTKBknsrsmdPmB1n3brwOP769aF/eF5eSLBNWTfn2G3bYObMAUyZAps2hfHAb789PGx06KFR/3VEpCmU3FtQzeTDa9fuS+Dx2x98EGbTqZGXF/qJV1SEpbKy9uvpkJPTly98IVyln3GGrtJFMlXakruZnQn8AsgF7nH3O9J1rtZk+/aQrGsSdvx63bras54D9O4dJm847bSwHjAA+vcP68MO2z+5VleHJF+T7OPX9ZUl8lrN2gy6dVvEl750csv9wUQkLdKS3M0sF/g1UAyUAq+Y2dPuvjId52tJlZW2X9KOX2/eXPv4zp1Doj7mGDjzzH2Ju3//0OxRM0tQonJyQk+VdI1hXlJygHndRCRjpOvKfRTwtruvBTCz2cB5QEqT+5IlYXjY5mhu171du8bWahpp1y7MktO/P0yeXDt5DxgQJjJWN0ERaWnpSu6HA+/H7ZcCJ8YfYGbTgemx3XIzW52mWFKtJ7D3+ryyEt55JyxZolb9sozqlrmyuX7J1K3BCRjTldzru1b1WjvuM4GZaTp/2pjZYncfGXUc6ZLN9VPdMlc21y9ddUtXX4hSoG/cfh/gwzSdS0RE6khXcn8FONrM+ptZe+Ai4Ok0nUtEROpIS7OMu1ea2TeAvxO6Qt7n7m+k41wRyLimpCbK5vqpbpkrm+uXlrqZuzd+lIiIZBQ9fygikoWU3EVEspCSe4LMrK+ZzTezVWb2hpldF3VMqWZmuWa21Mz+HHUsqWRm3czsMTN7M/bvl1XjK5jZt2P/Ta4ws4fNLD/qmJrLzO4zs01mtiKu7GAzm2tma2LrjJ0SpoH6/TT23+ZyM3vCzLql4lxK7omrBL7j7scCJwHXmtmgiGNKteuAVVEHkQa/AP7m7p8FhpJFdTSzw4FvASPdvYjQgeGiaKNKygPAmXXKbgTmufvRwLzYfqZ6gP3rNxcocvchwFvA91JxIiX3BLn7Bnd/Nba9nZAgDo82qtQxsz7A2cA9UceSSmbWBRgL3Avg7nvcfWu0UaVcO6CjmbUDDiKDnylx9+eALXWKzwMejG0/CJzfokGlUH31c/d/uHtlbHcR4bmgpCm5N4OZ9QOOB16KNpKU+jnwf4A0Dyrc4gYAHwH3x5qc7jGzTlEHlSru/gFwJ/AesAH4xN3/EW1UKVfo7hsgXGQBvSKOJ52uAp5JxQcpuTeRmRUAfwSud/dtUceTCmZ2DrDJ3ZdEHUsatAOGA//j7scDO8jsn/W1xNqfzwP6A4cBnczs0mijkuYwsx8Qmn9npeLzlNybwMzyCIl9lrs/HnU8KTQaONfM1gOzgdPN7PfRhpQypUCpu9f8ynqMkOyzxURgnbt/5O4VwOPAKRHHlGobzaw3QGy9KeJ4Us7MLgfOAb7sKXr4SMk9QWZmhHbbVe5+V9TxpJK7f8/d+7h7P8LNuGfdPSuu/tz9X8D7ZjYwVjSBFA89HbH3gJPM7KDYf6MTyKIbxjFPA5fHti8HnoowlpSLTWz078C57r4zVZ+r5J640cBXCFe1y2LL56MOShLyTWCWmS0HhgG3RxxPysR+kTwGvAq8Tvh/OmMf1Tezh4EXgYFmVmpmU4E7gGIzW0OYAChjZ3VroH6/AjoDc2N5ZUZKzqXhB0REso+u3EVEspCSu4hIFlJyFxHJQkruIiJZSMldRCQLKbmLiGQhJXcRkSz0/wHbcVhm+zR1HwAAAABJRU5ErkJggg==\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "Xval_add_one = np.insert(Xval,0,1,axis=1)\n",
    "plot_error_curve(X_add_one, y, Xval_add_one, yval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此图展示了，高偏差/欠拟合的现象。在高偏差/欠拟合的情况下，无论训练集有多大，误差都不会有太大的改观"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [],
   "source": [
    "def genPolyFeather(X, power):\n",
    "    Xpoly = X.copy()\n",
    "\n",
    "    for i in range(2,power+1):\n",
    "        Xpoly = np.insert(Xpoly, Xpoly.shape[1], np.power(Xpoly[:,1],i), axis=1)\n",
    "    \n",
    "    return Xpoly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_means_std(X):\n",
    "    means = np.mean(X, axis=0)\n",
    "    std = np.std(X,axis=0, ddof=1)\n",
    "    # 而且注意这里是样本标准差而不是总体标准差，使用np.std()时，\n",
    "    # 将ddof=1则是样本标准差，默认=0是总体标准差。而pandas默认计算样本标准差。\n",
    "    # ddof 是求方差中  分母 /(N - ddof)\n",
    "    return means, std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [],
   "source": [
    "def featureNormalize(X, means, std):\n",
    "    # 对样本进行标准化，而不是总标准化\n",
    "    X_norm = X.copy()\n",
    "    X_norm[:,1:] = (X[:,1:] - means[1:])/std[1:]\n",
    "\n",
    "    return X_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [],
   "source": [
    "def multi_learn_curve(multi_theta, power):\n",
    "    #多项式拟合曲线 以及误差分析图\n",
    "\n",
    "    xx = np.linspace(-75,55,50).reshape(-1,1)\n",
    "    xx_add_one = np.insert(xx, 0 ,1, axis=1)\n",
    "    xx_ploy = genPolyFeather(xx_add_one, power)\n",
    "    xx_means, xx_std = get_means_std(xx_ploy)\n",
    "    xx_norm = featureNormalize(xx_ploy, xx_means, xx_std)\n",
    "    yy = xx_norm @ multi_theta.T\n",
    "    # plt.figure(figsize=(8,2))\n",
    "    # plt.subplot(121)\n",
    "    plt.plot(X,y,'rx') #函数里的X是 带偏置项1\n",
    "    plt.plot(xx, yy, 'g--')\n",
    "    plt.xlabel('Change in water level(X)')\n",
    "    plt.ylabel('Water flowing out of the dam(y)')\n",
    "\n",
    "    # X_ploy =\n",
    "    # plt.subplot(122)\n",
    "    # plot_error_curve(xx_ploy, yy, xx_val_ploy,yy_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "power = 6\n",
    "l=0\n",
    "#特征缩放样本，求样本的均值和方差\n",
    "X_ploy = genPolyFeather(X_add_one,power)\n",
    "means,std = get_means_std(X_ploy)\n",
    "X_norm = featureNormalize(X_ploy, means, std)\n",
    "\n",
    "multi_theta = linear_trains(X_norm, y, l)\n",
    "\n",
    "multi_learn_curve(multi_theta, power)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "ValueError",
     "evalue": "could not broadcast input array from shape (21,6) into shape (21,1)",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-324-4a598aaa0432>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0my_ploy\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mX_ploy\u001b[0m \u001b[1;33m@\u001b[0m \u001b[0mmulti_theta\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mXval_ploy\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgenPolyFeather\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfeatureNormalize\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mXval_add_one\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmeans\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mstd\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mpower\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0myval_ploy\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mXval_ploy\u001b[0m \u001b[1;33m@\u001b[0m \u001b[0mmulti_theta\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-276-f9c9a6c16fa7>\u001b[0m in \u001b[0;36mfeatureNormalize\u001b[1;34m(X, means, std)\u001b[0m\n\u001b[0;32m      2\u001b[0m     \u001b[1;31m# 对样本进行标准化，而不是总标准化\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[0mX_norm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m     \u001b[0mX_norm\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mmeans\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mstd\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mX_norm\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: could not broadcast input array from shape (21,6) into shape (21,1)"
     ]
    }
   ],
   "source": [
    "y_ploy = X_ploy @ multi_theta.T\n",
    "\n",
    "Xval_ploy = genPolyFeather(featureNormalize(Xval_add_one,means,std),power)\n",
    "yval_ploy = Xval_ploy @ multi_theta.T\n",
    "\n",
    "plot_error_curve(X_ploy, y_ploy, Xval_ploy, yval_ploy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.6 64-bit ('base': conda)",
   "language": "python",
   "name": "python_defaultSpec_1595726451811"
  },
  "language_info": {
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "version": "3.7.6-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}